A245238 Decimal expansion of the Dickman function evaluated at 1/4.

0, 0, 4, 9, 1, 0, 9, 2, 5, 6, 4, 7, 7, 6, 0, 8, 3, 2, 3, 5, 2, 7, 3, 9, 1, 5, 0, 9, 2, 3, 6, 1, 5, 1, 8, 6, 0, 3, 2, 4, 8, 4, 2, 9, 7, 4, 1, 7, 6, 9, 2, 9, 4, 5, 9, 7, 7, 9, 6, 1, 6, 5, 7, 5, 2, 8, 0, 3, 0, 6, 3, 1

Offset: 0

Author

Charles R Greathouse IV, Jul 14 2014

Keywords

• nonn
• cons

Comments

Density of the fourth-root-smooth numbers.

Examples

			F(1/4) = 0.00491092564776083235273915092361518603248429741769294597796...
		

References

• Karl Dickman, On the frequency of numbers containing prime factors of a certain relative magnitude, Arkiv för Matematik, Astronomi och Fysik 22A 10 (1930), pp. 1-14.

Links

• David Broadhurst, Dickman polylogarithms and their constants arXiv:1004.0519 [math-ph], 2010.

Crossrefs

F(1/2) = A244009, F(1/3) = A175475.

Programs

Mathematica

RealDigits[1-Log[4]+PolyLog[2, 1/4]+2*Log[2]^2-Pi^2/12-PolyLog[3, 1/4]-PolyLog[2, 1/4]*Log[2]-2/3*Log[2]^3+13*Zeta[3]/24,10,100,-1][[1]] (* Vaclav Kotesovec, Jul 15 2014 *)

PARI

1-log(4)+polylog(2,1/4)+2*log(2)^2-Pi^2/12-polylog(3,1/4)-polylog(2,1/4)*log(2)-2/3*log(2)^3+13*zeta(3)/24